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A163307 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8. 3
1, 8, 68, 600, 5408, 49312, 452416, 4164096, 38391040, 354254336, 3270354944, 30197778432, 278873280512, 2575523676160, 23786907123712, 219693657980928, 2029087298289664, 18740701224894464, 173089976023777280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A163306. Inverse binomial transform of A163308.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (14,-44).

FORMULA

a(n) = ((5+sqrt(5))*(7+sqrt(5))^n + (5-sqrt(5))*(7-sqrt(5))^n)/10.

G.f.: (1-6*x)/(1-14*x+44*x^2).

E.g.f.: (1/5)*exp(7*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016

MATHEMATICA

LinearRecurrence[{14, -44}, {1, 8}, 50] (* G. C. Greubel, Dec 18 2016 *)

PROG

(MAGMA) [ n le 2 select 7*n-6 else 14*Self(n-1)-44*Self(n-2): n in [1..19] ];

(PARI) Vec((1-6*x)/(1-14*x+44*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016

CROSSREFS

Cf. A163306, A163308.

Sequence in context: A249390 A190510 A282563 * A281337 A152105 A068766

Adjacent sequences:  A163304 A163305 A163306 * A163308 A163309 A163310

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Jul 24 2009

STATUS

approved

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Last modified May 10 14:32 EDT 2021. Contains 343771 sequences. (Running on oeis4.)